Inverse synthetic aperture radar (ISAR) imaging of maneuvering target is a main topic in the field of radar signal processing, and the received signal in a range bin can usually be characterized as multicomponent cubic chirps with constant amplitudes after motion compensation. In fact, the phenomenon of migration through resolution cell (MTRC) often occurs for the target’s complex motion, and this will induce the time-varying character for the amplitudes of cubic chirps. An algorithm for the parameters estimation of multicomponent cubic chirps with time-varying amplitudes based on the extension form of match Fourier transform is proposed, and by using it in ISAR imaging of maneuvering target, the quality of images can be improved significantly compared with the constant amplitudes model. Results of simulated and real data validate the effectiveness of the algorithm in this paper.